Question: Solve for $x$ and $y$ using elimination. $\begin{align*}6x-3y &= 9 \\ -6x+2y &= -7\end{align*}$
We can eliminate $x$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-y = 2$ Divide both sides by $-1$ and reduce as necessary. $y = -2$ Substitute $-2$ for $y$ in the top equation. $6x-3( -2) = 9$ $6x+6 = 9$ $6x = 3$ $x = \dfrac{1}{2}$ The solution is $\enspace x = \dfrac{1}{2}, \enspace y = -2$.